Question: Christopher is 4 times as old as Michael. Ten years ago, Christopher was 9 times as old as Michael. How old is Christopher now?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Michael. Let Christopher's current age be $c$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $c = 4m$ Ten years ago, Christopher was $c - 10$ years old, and Michael was $m - 10$ years old. The information in the second sentence can be expressed in the following equation: $c - 10 = 9(m - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = c / 4$ . Substituting this into our second equation, we get: $c - 10 = 9($ $(c / 4)$ $- 10)$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $c - 10 = \dfrac{9}{4} c - 90$ Solving for $c$ , we get: $\dfrac{5}{4} c = 80$ $c = \dfrac{4}{5} \cdot 80 = 64$.